It’s a matter of some irony that forces that act across larger distances also give rise to lots of empty space – although the more you think about it, the more it makes sense. The force of gravity, for example, can act across millions of kilometres but this only means two massive objects can still influence each across this distance instead of having to get closer to do so. Thus, you have galaxies with a lot more space between stars than stars themselves.
The electromagnetic force, like the force of gravity, also follows an inverse-square law: its strength falls off as the square of the distance – but never fully reaches zero. So you can have an atom with a nucleus of protons and neutrons held tightly together but electrons located so far away that each atom is more than 90% empty space.
In fact, you can use the rules of subatomic physics to make atoms even more vacuous. Electrons orbit the nucleus in an atom at fixed distances, and when an electron gains some energy, it jumps into a higher orbit. Physicists have been able to excite electrons to such high energies that the atom itself becomes thousands of times larger than an atom of hydrogen.
This is the deceptively simple setting for the Rydberg polaron: the atom inside another atom, with some features added.
In January 2018, physicists from Austria, Brazil, Switzerland and the US reported creating the first Rydberg polaron in the lab, based on theoretical predictions that another group of researchers had advanced in October 2015. The concept, as usual, is far simpler than the execution, so exploring the latter should provide a good sense of the former.
The January 2018 group first created a Bose-Einstein condensate, a state of matter in which a dilute gas of particles called bosons is maintained in an ultra-cold container. Bosons are particles whose quantum spin takes integer values. (Other particles called fermions have half-integer spin). As the container is cooled to near absolute zero, the bosons begin to collectively display quantum mechanical phenomena at the macroscopic scale, essentially becoming a new form of matter and displaying certain properties that no other form of matter has been known to exhibit.
Atoms of strontium-84, -86 and -88 have zero spin, so the physicists used them to create the condensate. Next, they used lasers to bombard some strontium atoms with photons to impart energy to electrons in the outermost orbits (a.k.a. valence electrons), forcing them to jump to an even higher orbit. Effectively, the atom expands, becoming a so-called Rydberg atom. In this state, if the distance between the nucleus and an excited electron is greater than the average distance between the other strontium atoms in the condensate, then some of the other atoms could technically fit into the Rydberg atom, forming the atom-within-an-atom.
 Rydberg atoms are called so because many of their properties depend on the value of the principal quantum number, which the Swedish physicist Johannes Robert Rydberg first (inadvertently) described in a formula in 1888.
Rydberg atoms are gigantic relative to other atoms; some are even bigger than a virus, and their interactions with their surroundings can be observed under a simple light microscope. They are relatively long-lived, in that the excited electron decays to its ground state slowly. Astronomers have found them in outer space. However, Rydberg atoms are also fragile: because the electron is already so far from the nucleus, any other particles in the vicinity, even a weak electromagnetic field or a slightly warmer temperature could easily knock the excited electron out of the Rydberg atom and end the Rydberg state.
Some clever physicists took advantage of this property and used Rydberg atoms as sensitive detectors of single photons of light. They won the Nobel Prize for physics for such work in 2011.
However, simply sticking one atom inside a Rydberg atom doth not a Rydberg polaron make. A polaron is a quasiparticle, which means it isn’t an actual particle by itself, as the –on suffix might suggest, but an entity that scientists study as if it were a particle. Quasiparticles are thus useful because they simplify the study of more complicated entities by allowing scientists to apply the rules of particle physics to arrive at equally correct solutions.
This said, a polaron is a quasiparticle that’s also a particle. Specifically, physicists describe the properties and behaviour of electrons inside a solid as polarons because as the electrons interact with the atomic lattice, they behave in a way that electrons usually don’t. So polarons combine the study of electrons and electrons-interacting-with-atoms into a single subject.
Similarly, a Rydberg polaron is formed when the electron inside the Rydberg atom interacts with the trapped strontium atom. While an atom within an atom is cool enough, the January 2018 group wanted to create a Rydberg polaron because it’s considered to be a new state of matter – and they succeeded. The physicists found that the excited electron did develop a loose interaction with the strontium atoms lying between itself and the Rydberg atom’s nucleus – so loose that even as they interacted, the electron could still remain part of the Rydberg atom without getting kicked out.
In effect, since the Rydberg atom and the strontium atoms inside it influence each other’s behaviour, they altogether made up one larger complicated assemblage of protons, neutrons and electrons – a.k.a. a Rydberg polaron.